OPTION A 1. A faculty employs 75 lecturers. The table below summaries their length of service at the faculty, categorized by gender. Less than 3 years 3 years to 8 years More than 8 years Female 12 20 Male 8 15 7 a) Find the probability that a randomly selected lecturer: i. is female (1 marks) ii. is female, given that the lecturer has more than 8 years service (1 marks) iii. is male, given that the lecturer has less than 3 years service (1 marks) b) State, giving a reason, whether or not the event of selecting a male lecturer is independent of the event of selecting a lecturer with less than 3 years service. (2 marks) c) Three lecturers are selected at random without replacement. Find the probability that all three are: i. females with less than 3 years service (2 marks) ii. of the same gender